Partial Likelihood Function for the Cox Model

Let denote the distinct, ordered event times. Let denote the multiplicity of failures at ; that is, is the size of the set of individuals that fail at . Let be the weight associated with the th observation unit in the th cluster in stratum . Using this notation, the pseudo-likelihood functions used in PROC SURVEYPHREG to estimate are described in the following sections.

Continuous Time Scale

Let denote the risk set just before the th ordered event time .

The Breslow likelihood is expressed as


The Efron likelihood is expressed as


where is